Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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EF, ducta, vtcunque quadratum, EI, detractum à rectangulo ſub,
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IE, EF, relinquit rectangulum ſub, EI, IF, ita in cæteris ſequitur;
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<
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">& </
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<
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xml:space
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">illis ſimul collectis ſequitur etiam, quod detractis omnibus qua-
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pro C.23.
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lib.2.</
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dratis ſemiportionis, OCD, à rectangulis ſub parallelogrammo, O
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V, & </
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tione, OCD, & </
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<
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">trilineo, DCV, ad hæc igitur, quæ ſunt dictum
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reſiduum, omnia quadrata parallelo-
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grammi, OV erunt vt parallelogram-
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mum, OV, adreſiduum ſemiportio-
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nis, OCD, ab ea demptis, {2/3}, paral-
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lelogrammi, OV; </
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<
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">eadem autem om-
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nia quadrata parallelogrammi, OV,
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ad rectangula ſub parallelogrammo.
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</
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<
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lib.2.</
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omnia quadrata ſemiportionis, OC
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D, vna cum rectangulis ſub ſemipor-
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tione, OCD, & </
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<
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">trilineo, CVD,
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ſunt vt parallelogrammum, OV, ad
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ſemiportionem, OCD, vt paulò ſupra in hac demonſtratione oſten-
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dimus, ergo, colligendo, omnia quadrata parallelogrammi, OV,
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ad omnia quadrata ſemiportionis, OCD, vna cum rectangu is bis
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ſub ſemiportione, OCD, & </
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<
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">trilineo, CVD, ſumptis, erunt vt pa-
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rallelogrammum, OV, ad ſemiportionem, OCD, vna cum exceſ-
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ſu, quo dicta ſemiportio, OCD, excedit, {2/3}, parallelogrammi, O
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V, ergo, perconuerſionem rationis, omnia quadrata parallelogram-
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mi, OV, ad omnia quadrata trilinei, DCV, quæ remanent detra-
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lib. 2.</
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ctis omnibus quadratis ſemiportionis, OCD, vna cum rectangulis
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ſub illa, & </
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parallelogrammi, OV; </
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ctangulo bis ſub, EI, IF, remanet quadratum, IF,) ad omnia qua-
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dratatrilinei, DCV, erunt vt parallelogrammum, OV, adreſiduum,
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detracta ſemiportione, OCD, vna cum exceſſu, quoipſa ſuperat
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duas tertias parallelogrammi, OV, à dicto parallelogrammo,
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OV.</
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<
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proximè, vt 21. </
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eſſe 21. </
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eſt .</
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">adeam, ſicut rectangulum, quod eſſet circulo, vel ellipſi, A
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BCD, circumſcriptum, habens latera ipſis, AC, BD, axibus pa-
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rallela ad eundem circulum, vel ellipſim .</
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oſtendit Archimedes lib. </
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